Connection To Ricci Flow
For more details on this relationship, see Ricci flow#Relationship_to_uniformization_and_geometrization.In introducing the Ricci flow, Richard Hamilton showed that the Ricci flow on a closed surface uniformizes the metric (i.e., the flow converges to a constant curvature metric). However, his proof relied on the uniformization theorem. Xiuxiong Chen, Peng Lu, and Gang Tian (2006) showed that it is nevertheless possible to prove the uniformization theorem via Ricci flow.
Read more about this topic: Uniformization Theorem
Famous quotes containing the words connection to, connection and/or flow:
“One must always maintain one’s connection to the past and yet ceaselessly pull away from it. To remain in touch with the past requires a love of memory. To remain in touch with the past requires a constant imaginative effort.”
—Gaston Bachelard (1884–1962)
“We say that the hour of death cannot be forecast, but when we say this we imagine that hour as placed in an obscure and distant future. It never occurs to us that it has any connection with the day already begun or that death could arrive this same afternoon, this afternoon which is so certain and which has every hour filled in advance.”
—Marcel Proust (1871–1922)
“But even suppose blood should flow. Is there not a sort of blood shed when the conscience is wounded? Through this wound a man’s real manhood and immortality flow out, and he bleeds to an everlasting death. I see this blood flowing now.”
—Henry David Thoreau (1817–1862)